Question

A bird leaves its nest and travels 18 miles per hour downwind for x hours. On the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours.

a. What is the distance of the entire trip? (In miles)

b. How long does the entire trip take? (In hours and minutes and seconds)

Answer 1

9514 1404 393

Answer:

• 60 miles
• 3 hours 40 minutes 0 seconds

Explanation:

The relation between speed, distance, and time is ...

distance = speed × time

a) The distance the bird traveled downwind is ...

(18 miles/hour)(x hours) = 18x miles

3 miles per hour slower than 18 miles per hour is 15 miles per hour. So the distance in miles the bird traveled after x hours on the return trip is ...

15x = 18x -5

5 = 3x . . . . . . add 5 -15x

x = 5/3 . . . . . .divide by 3

Then the distance traveled downwind is ...

18x = 18(5/3) = 30 . . . . miles

and the time for the return trip is ...

(30 mi)/(15 mi/h) = 2 h . . . . . for the entire return trip

So, the entire round trip is 2×30 miles = 60 miles.

__

b) The time for the entire trip is ...

5/3 h downwind + 2 h return = 3 2/3 h = 3 hours 40 minutes 0 seconds